Improved particle swarm optimization for strong ground motion combination

A step-by-step numerical solution to dynamic or nonlinear systems depends on the inputtime history record of the strong ground motion. Well-known seismic design codesrecommend using a set of scaled records instead of only one. That is because a singleinput motion is not reliable enough to cover the seismic characteristics of all possibleearthquakes for engineering design purposes. As a current state of practice, the scaling coefficients are taken similar and the result does not necessarily lead to a close compatibility of the resulted mean spectrum with the standard target. In this regard, the coefficients as floating-point numbers should be searched in the form of an optimization problem. Such a problem deals with a continuous type of search space with an infinite number of points. Thus complex optimizer engines are required to deal with it and seek a true global optimum set of scaling coefficients in order to suitably combine the selected ground motion records for further seismic design purposes. Particle Swarm Optimization, PSO, is one of the multi-agent meta-heuristic methods successfully applied to a variety of engineering design problems. The present work formulates the problem of seeking optimal scaling factors using a utilized version of swarm intelligence as this method is best suited for continuous search spaces. In addition to inertial, cognitive and social terms of design point directions, an extra term is also utilized to improve the algorithm performance. In the first case, it is a new design vector with its elements selected one by one from other vectors in the current population of the swarm particles. The second modification is ordinating the velocity vector toward a randomly re-initiated particle position. In addition to the standard form of the particle swarm optimization, the aforementioned PSO versions are thus utilized, employed and further compared in the present work. A variety of real-world ground motion records are picked from an available earthquake. The target spectrum is selected according to the Iranian Standard No.2800 for the soil type III and five percent damping considering the case of practical building structures. For each earthquake, the response spectra are generated for its longitude and transverse excitations and then combined using the Square Root of Sum of Squares (SRSS) method. The resulting SRSS acceleration response spectra are then averaged with the scaling factors with respect to the design target assigned by the developed optimization algorithms. For the sake of true comparison, the same control parameters are chosen for three proposed versions of PSO, taken 2 for all the social, cognitive and extra congregation or combinatorial term except for the inertial coefficient which is taken 0.4. An error function is also defined to evaluate the compatibility of such weighted average spectrum with the target. The optimizer then samples various combinations of the scaling coefficients for the SRSS spectra and evaluated the error function for every such set. It seeks the optimal set among the continuous search space using the utilized artificial swarm intelligence for a pre-assigned number of particles and algorithm iterations. Consequently, the achieved results in the treated example show superiority of the optimized set over those in the code practice and considerable convergence/effectiveness improvement in the proposed methods over the standard particle swarm optimization.